fuels oxidation chemistry

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© 2005 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved.

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Fuels oxidation chemistryFuels oxidation chemistry

Module B, Section 3This course was developed by:• Edward S. Blurock (Lund University)• Gladys Moréac (Lund University)

An EC funded NoE on Energy Conversion in Engines

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OutlineMechanism Generation

– Reactive Center and Reaction Generation

– Complete Mechanism Generation

– Optimization

Mechanism Reduction

– Lumping

– Skeletal

– Phase Optimized Mechanisms

– QSSA Reduced Mechanisms

– Tabulation Methods

Mechanism Optimization

– Automatic Reaction Coefficient Optimization

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Mechanism GenerationSingle Reaction Generation

– Generic Reaction Classes

Definition of Reactive Center and Environment

– Application of Reaction Class to Species

Recognition of reactive center

Application of bond/valence changes

Reaction Pathways

– Sub-Mechanisms

Complete Mechanism Generation

– Exhaustive Application of Reaction Classes

Filtering of unwanted reactions

– Controlled Generation

Generate only a fixed path of reactions

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Mechanism GenerationWhy automatic generation?

– Detailed mechanisms of large hydrocarbons too large and too complex now to do by hand

Hundreds to thousands of species and reactions

– Automation is another level of thinking

Not thinking of individual species and reactions

Rather classes of species and reactions

Classes:

– Groups of reactions and species with similar properties

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Single Reaction GenerationKey Concept

Reaction Center

The set of bonds and atom valences that change in the course of a reaction

Generic Loss of Radical to Form Olefin

Generic Group Replaced by an Oxygen

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Single Reaction GenerationReaction Pattern

Supplemented with the Environment around Center

(Functional Groups which can effect reaction rate)

Peroxyl Group Influence on bonding

Include Bonding of Carbon

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Single Reaction GenerationCorrespondence Between Reactants and Products

Determines how the bonding and atom valences are changed in the course of the reaction

The Reactive Center ChangesThe surrounding functional Groups are unchanged

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Single Reaction GenerationReaction Formation

Match Reactant of Reaction Pattern with Reactant

Correspondence to Pattern

Rest of Reactant

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Single Reaction GenerationReaction Formation

Change as Specified in the Reactive CenterThe changes specified by the Pattern

Are Performed on the Reactant

CH3CH2CH2CHCH2OOH CH3CH2CHCH2 OOH+

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Reaction Pathways

– Sub-Mechanisms






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Reaction PathwayR + O = R. +OH

R. + O2 = ROO.

ROO. = .QOOH

.QOOH + O2 = OOQOOH

OOQOOH = OQOOH

OQOOH = products + OH

CH3CH2CH2CH3 + O = .CH2CH2CH2CH3

CH2CH2CH2CH3 + O2 = OOCH2CH2CH2CH3

.OOCH2CH2CH2CH3 = HOOCH2CHCH2CH3

HOOCH2CHCH2CH3 = HOOCH2CH(OO)CH2CH3

HOOCH2CH(OO)CH2CH3 = CHOC(OOH)CH2CH3 + OH

CHOC(OOH)CH2CH3 = OH + products

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Reaction PathwayA Sequence generates a sub-mechanism tree of reactions

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Reaction Pathways

– Sub-Mechanisms






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Generation of MechanismThe Problem of the Combinatorial Explosion

In principle

everything can react with everything

in a multitude of ways

A large part of detailed mechanism production

Is deciding what is important and what is not

The decision of how large the mechanism can be depends on how it is going to be used.

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Generation of MechanismMultiple Applications of Reaction Classes on Species

Question:On which species do you apply the reaction classes?

• Exhaustive with Filtering: Apply the reaction classes to all species. Filter out

unreasonable reactions. Repeat on the all products.

• Controlled: Define a set of sequences of reaction classes. Apply the seed molecule to the first reaction class. For the rest, only apply the previous products to

the next reaction class in the sequence.

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Exhaustive with FilteringFor all reaction classes

For all species currently present

Generate a Single Reaction

Determine whether reaction is reasonableYes: Add products to next list of species and add reaction to

list of reactions

No: Add Nothing

In a sense, this is the way ‘nature’ does it.

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Exhaustive with FilteringThe key to the success of this is the filtering out of

unreasonable reactions.This is closer to what nature does

(nature’s filter is, of course, perfect).

Can create very large mechanisms(depending on filter/accuracy)

These are biased by the modeler only in the description of the reaction classes.

Complete chemistry is described.Could enhance prediction and new pathways

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Exhaustive with FilteringExample: NETGEN

Rate-Based Generation Criterion– Rchar : Characteristic rate (maximum rate of formation of all species)

– Rmin = Rchar : Minimum rate allowed (determines range)

– Species kept in mechanism if rate of formation greater than Rmin

Examples: De Witt, M.J., Dooling, D.J., Broadbelt, L.J, Ind. Eng. Chem. Res., 39, 2228-2237 (2000)

– Tetradecane pyrolysis: large extensive mechanisms

Grenda J.M., Androulaktis, I.P., Dean, A.M., Green Jr., W.H., Ind. Eng. Chem. Res,42, 1000-1010 (2003)

– Pressure dependent reactions through cycloalkyl intermediates

– Use of Quantum Rice-Ramsperger-Kassel (QRRK) for pressure dependence

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Controlled GenerationA. Define a set of reaction pathways to make up the mechanism

B. Establish the set of seed molecules

C. For each seed and each pathway :

1. Apply the seed species to the first step of pathway

2. Apply the products of the last step to the next step in the pathway

3. Repeat 2 until no more steps in the pathway

4. The set of species and reactions make up this sub-mechanism

D. Combine the set of sub-mechanisms together to form the final generated mechanism

1. Check for species and reaction correspondences between submechanisms

2. Include only the unique set of species and reactions

E. Combine the final generated mechanism with Base mechanism

1. Check for species and reaction correspondences between submechanisms

2. Include only the unique set of species and reactions

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Controlled GenerationEach Pathway Represents a Submechanism

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Controlled GenerationA

seed molecule

applied to a specific

Pathway

Is a

Sub-Mechanism

All the sub-mechanisms are combined into one

Generated mechanism

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Controlled Generation• Efficient and Compact Mechanisms:

– Controlled Generation allows complex chemistry to be introduced with relatively small mechanisms for large hydrocarbons

• Interactive Artificial Intelligence Approach

– It basically mimics how a modeler would generate a mechanism by hand

– The processes are automated

– The details are left to the automation process

• Higher Level of Thinking

– Modeler thinking in terms of classes of species and reactions

– The mechanism is organized in pathways and submechanism

– The individual reactions are transparent to the modeler

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– Optimization

Mechanism Reduction

– Lumping

– Skeletal






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Mechanism ReductionThere is a trade-off between complexity and detail of

model and computational time.

Often mechanisms are used to calculate the chemical source terms within larger more complex computations

(Computational Fluid Dynamics)

Goal:

Transform to computationally simpler form

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Mechanism ReductionGoal: To reproduce the details of the complex mechanism in an equivalent

small mechanism.

Techniques:

– Condense: Condense the information to a computationally compact form (Lumping)

– Limit Conditions: Under a limited set of conditions, eliminate unused portions of the mechanism are eliminated (Skeletal,POSM)

– Tabulation: In local regions of source term space, approximations are tabulated (PRISM, ISAT, Flamelets)

– Reformulate: Reformulation of the source term equations to computationally simpler form (QSSA, CSP)

– Progress Variables: Use of a reduced number of coordinates to access source term state information

– Combinations: Hybrids of the above

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– Optimization

Mechanism Reduction

– Lumping

– Skeletal






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Mechanism Reduction: LumpingFor the most part, the calculation of the differential equations associated with source terms goes with the

cube of the number of species involved.

Reduce the number of species by combining

equivalent species together

The definition of equivalent

depends on the level of modeling

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Lumped species in n-heptane MechanismSchematic representation for the lumping of four different

5-ring alkylperoxy radicals

5r-C7H14OOH

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Lumped species in n-heptane Mechanism

6r-QOOH Species RO2 Species

p = 40bar, = 1.0, T = 800K

0

5 10-5

1 10-4

2 10-4

0.27 0.29 0.31 0.33 0.35

1-C7H

15O

22-C

7H

15O

23-C

7H

15O

24-C

7H

15O

2Added SpeciesL-C

7H

15O

2

Con

cen

trat

ion

[m

ole

/cm

3]

t [msec]

0

4 10-7

8 10-7

1 10-6

2 10-6

0.27 0.29 0.31 0.33 0.35

C7H

14OOH1-3

C7H

14OOH2-4

C7H

14OOH3-1

C7H

14OOH3-5

C7H

14OOH4-2

Added Species6r-C

7H

14OOH

Con

cen

trat

ion

[m

ole

/cm

3]

t [msec]

Concentration of Species Lumped Together Add to Single Lumped Species

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1362 reactions142 species

n-C7H16

L-C7H15

L-C7H15O2

A-5r

B-5r

C-5r

D-5r

A-6r

B-6r

C-6r

D-6r

A-7r

B-7r

C-7r

D-7r

A-8r

B-8r

C-8r

D-8r

L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring

Lumped Mechanism : n-heptane

A1-2 A4-3

B3-4

C4-3

D4-3

n-C7H16

4- C7H15O2

1-C7H15 4-C7H15

1-C7H15O2 2- C7H15O2 3- C7H15O2

2-C7H15 3-C7H15

A1-3 A1-4 A1-5 A2-1 A2-3 A2-4 A2-5 A2-6 A3-2 A3-4 A3-5 A3-6 A3-7 A3-1 A4-2 A4-1

B1-3 B1-4 B1-5 B1-2 B1-2 B2-3 B2-4 B2-5 B2-6 B1-3 B2-3 B3-4 B3-5 B2-5 B1-5 B1-4 B2-4

C1-3 C1-4 C1-5 C2-1 C2-3 C2-4 C2-5 C2-6 C3-1 C3-2 C3-4 C3-5 C3-6 C3-7 C4-1 C4-2

D1-3 D1-4 D1-5 D2-1 D2-3 D2-4 D2-5 D2-6 D3-1 D3-2 D3-4 D3-5 D3-6 D3-7 D4-1 D4-2 D1-2

C1-2

1624 reactions203 speciesDetailed

1-2 = 1 position of OOH and 2 is radical site

A = C7H14OOH, B = HOO-C7H14O2, C = O-C7H13OOH and D = Carbonyl + OH

A1-2 A4-3

B3-4

C4-3

D4-3

n-C7H16

4- C7H15O2

1-C7H15 4-C7H15

1-C7H15O2 2- C7H15O2 3- C7H15O2

2-C7H15 3-C7H15





C1-2


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Lumped Mechanism – Same As Detailed

Davis and Law

Laminar flame speed for n-heptane/air mixture at p=1 bar and Ti=298 K

Experimental data (symbols)Detailed mechanism (solid line)

Lumped mechanism (dashed line)

10

20

30

40

50

0.6 0.8 1.0 1.2 1.4 1.6 1.8

Davis & LawLund_CalculationsB

SL [

cm/s

ec]

n-heptane-air

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– Optimization

Mechanism Reduction

– Lumping

– Skeletal






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Mechanism Reduction: SkeletalValidity under Limit Conditions

Under a limited set of conditions

(which can be quite extensive),

unused species of the mechanism are eliminated

Unused Criteria

Through post-processing of detailed mechanism

determine the species which, if eliminated

will not effect the final results

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Skeletal Mechanisms: Criteria

Reaction flow analysis

Gives the atomic mass flow through the given reactions.

Sensitivity Analysis

Finds important (sensitive) species for the wanted results.

Necessity Analysis:

A single parameter indicating the extend a species is used within a mechanism

Based on:

If a species is determined to be ‘not necessary’ for entire range of validity, then it is eliminated from the mechanism

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470 reactions 64 species

n-C7H16

L-C7H15

L-C7H15O2

A-5r

B-5r

C-5r

D-5r

A-6r

B-6r

C-6r

D-6r

A-7r

B-7r

C-7r

D-7r

Skeleton Mechanism : n-heptane

A1-2 A4-3

B3-4

C4-3

D4-3

n-C7H16

4- C7H15O2

1-C7H15 4-C7H15

1-C7H15O2 2- C7H15O2 3- C7H15O2

2-C7H15 3-C7H15





C1-2


Lumped

n-C7H16

L-C7H15

L-C7H15O2

A-5r

B-5r

C-5r

D-5r

A-6r

B-6r

C-6r

D-6r

A-7r

B-7r

C-7r

D-7r

A-8r

B-8r

C-8r

D-8r



n-C7H16

L-C7H15

L-C7H15O2

A-5r

B-5r

C-5r

D-5r

A-6r

B-6r

C-6r

D-6r

A-7r

B-7r

C-7r

D-7r

A-8r

B-8r

C-8r

D-8r


n-C7H16

L-C7H15

L-C7H15O2

A-5r

B-5r

C-5r

D-5r

A-6r

B-6r

C-6r

D-6r

A-7r

B-7r

C-7r

D-7r

A-8r

B-8r

C-8r

D-8r

n-C7H16

L-C7H15

L-C7H15O2

A-5r

B-5r

C-5r

D-5r

A-6r

B-6r

C-6r

D-6r

A-7r

B-7r

C-7r

D-7r

A-8r

B-8r

C-8r

D-8r



n-C7H16

L-C7H15

L-C7H15O2

A-5r

B-5r

C-5r

D-5r

A-6r

B-6r

C-6r

D-6r

A-7r

B-7r

C-7r

D-7r

A-8r

B-8r

C-8r

D-8r



Lumped

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– Optimization

Mechanism Reduction

– Lumping

– Skeletal






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Mechanism Reduction: POSM

Phase Optimized Skeletal MechanismRecognition that a combustion process goes through phases

and in each phase an even more reduced skeletal mechanism used

– Phases determined automatically through machine learning clustering techniques with necessity parameter as base

– Simple recognition function to determine in which phase the process is in is determined by a decision tree machine learning technique

– Results translated to FORTRAN routines

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Phase Optimized Skeletal Mechanism

Heptane-Toluene Mechanism

Original Full Skeleton Mechanism 126 Species

Five Combustion Phases Determined

– Initial Phase: 76 Species

– Pre-Ignition: 85 Species

– Ignition Phase Before: 90 Species

– Ignition Phase After: 100 Species

– Post Ignition Phase: 51 Species

Speed up factor of 3 to 10

Tunèr, M., Blurock, E. S. and Mauss, F., Accepted for publication in conference, Power Train and Fluid Systems, SAE 2005.

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Mechanism Reduction: Tabulation

Divide up source term space into very local regions and use a local approximation for each region

– Build up set of local regions dynamically during calculation

If a new point, set up a local approximation

If an existing point, use approximation

– Dynamically set up a tree search structure to address local regions

Given a point, the tree search structure allows efficient access to appropriate local approximation

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– Optimization

Mechanism Reduction

– Lumping

– Skeletal






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Quasi-Steady State AssumptionClass of Methods: Time Scale Decomposition

– Separation of fast and slow processes

– Fast processes of full phase space fall into (slow) lower dimensional manifold

– Decoupling (two sets of equations) of system into fast and slow modes

Quasi-Steady State Assumption:

– Some Species are in equilibrium (dC/dt=0)

Formation and Consumption are relatively fast reactions

– Their solution can be calculated algebraically instead of solving the differential equations

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– Optimization

Mechanism Reduction

– Lumping

– Skeletal






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Mechanism Reduction: Tabulation

– ISAT: First Order Polynomial Approximation

Pope, S., Combust. Theory Modelling 1:41-63 (1997) – PRISM: Second Order Polynomial Approximation

Frenklach, M., Wang, H. and Rabinowitz, M., Energy Combust. Sci 18:47-73 (1992)

Blurock, E. S., Lehtiniemi, H., Mauss, F. and Gogan, A., Berichte der Energie und Varfahrenstechnik (2005)

– Combination: First and Second Order Combined

Ebenezer, N., Blurock, E. S. and Mauss, F.,4th Mediterranean Combustion Symposium (2005)

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– Optimization

Mechanism Reduction

– Lumping

– Skeletal






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Optimization of Rate Coefficients

Frequency Factor Temperature Exponent

Activation Energy

S

kki

N

ik

nkik RTETAcr exp,

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Optimization of Rate Coefficients

j

N

i

N

jiiij

N

ii

N

iii XXXX

R RR

i

R

20φy

N

rr

obsrr

1

2θyyθΨ

Frenklach, M., Wang H. and Rabinovitz, M. J., "Optimization and Analysis of Large Chemical Kinetic Mechanism using the Solution Mapping Method - Combustion of Ethane".Prog. Energy Combustion Sci., 1992. 18: p. 47-73.

Function to Optimize

Model – Experimental Data

Response Surface

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Reduction-Optimization Cycle

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1

2

3

4

5

6

25 30 35 40 45 50 55 60

Tim

e [s

ec]

Erro

r [CA

D]

# Species

CPU Time

Reduction

Op

timiz

atio

n

Op

timiz

atio

n

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Reduction-Optimization Cycle

-5

0

5

10

15

20

-2 -1 0 1 2 3 4 5 6

Experiment [CAD]

Sim

ulat

ion

[C

AD

] Experiment (line), Original (black dots), Optimized (red triangles), Over-Reduced (white dots)Re-Optimized (purple x) target values.

fuels oxidation chemistry

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